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Grade 11 · Trigonometry
Trigonometric Graphs (Grade 11)
MEMORANDUM
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  / 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

  1. 1
    Write down the amplitude of y = 2 sin x.
    (2)
    -360°-180°180°360°-2-112xyy = sin xy = 2 sin x
    2✓✓ (2)
  2. 2
    Write down the period of y = sin 2x.
    (2)
    -360°-180°180°360°-11xyy = sin xy = sin 2x
    360°2 = 180°✓✓ (2)
  3. 3
    Write down the range of y = 2 sin x.
    (2)
    −2 ≤ y ≤ 2✓✓ (2)
  4. 4
    Describe the transformation from y = cos x to y = cos(x + 60°).
    (2)
    -360°-180°180°360°-11xyy = cos xy = cos(x + 60°)
    A shift of 60° to the left✓✓ (2)
  5. 5
    Write down the period of y = tan 2x.
    (2)
    180°2 = 90°✓✓ (2)
  6. 6
    Write down the equations of the asymptotes of y = tan x for x ∈ [0° ; 360°].
    (2)
    -360°-180°180°360°-4-224xyy = tan x
    x = 90° and x = 270°✓✓ (2)
  7. 7
    How many complete cycles does y = sin 2x complete in [0° ; 360°]?
    (2)
    2✓✓ (2)
  8. 8
    Write down the range of y = tan x.
    (2)
    y ∈ ℝ✓✓ (2)
TOTAL: 16 marks
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